Consider an infinitely long straight conductor carrying a current. Let's assume that the free charges in the conductor are positive and are moving at a drift velocity v. Now, consider a particle of charge +q also moving with v in the same direction as the current at a distance r from the conductor. It faces two separate forces: One due to electrostatic repulsion from the charges in the wire and another because the wire has a magnetic field and a moving particle in a magnetic field experiences a force. The magnetic force points radially towards the wire and electrostatic repulsion points away from the wire. Now, think of this in a frame which is moving at v in the same direction as the current. In this frame, the conductor no longer has a current; it is now just a straight piece of conductor with charge. The particle is also at rest in this frame. The only force it faces is electrostatic repulsion. The magnitude of this repulsive force does not change. So the two frames predict different answers to what is going to happen to the particle. Where am I going wrong?